Loudspeaker system with controlled directional sensitivity

ABSTRACT

Loudspeaker system having various loudspeakers (SP i , i=0, 1, 2, . . . , m) which are arranged in accordance with a predetermined pattern and have associated filters (F i , i=0, 1, 2, . . . , m), which filters all receive an audio signal (AS) and are equipped to transmit output signals to the respective loudspeakers (SP i ) such that they, during operation, generate a sound pattern of a predetermined form, wherein the loudspeakers (SP i ) have a mutual spacing (l i ), which, insofar as physically possible, substantially corresponds to a logarithmic distribution, wherein the minimum spacing is determined by the physical dimensions of the loudspeakers used.

The invention relates to a loudspeaker system comprising variousloudspeakers which are arranged in accordance with a predeterminedpattern and have associated filters, which filters all receive an audiosignal and are equipped to transmit output signals to the respectiveloudspeakers such that they, during operation, generate a sound patternof a predetermined form.

A loudspeaker system of this type is disclosed in U.S. Pat. No.5,233,664. The system described in said patent comprises m loudspeakersand N microphones, which are arranged predetermined distances away fromthe loudspeakers. Each loudspeaker receives an input signal from aseparate series circuit of a digital filter and an amplifier. Each ofsaid series circuits receives the same electrical input signal, whichhas to be converted into an acoustic signal. The digital filters havefilter coefficients which are adjusted by a control unit, whichreceives, inter alia, output signals from the microphones. Theloudspeakers are arranged in a predetermined manner. The objective is tobe able to generate a predetermined acoustic pattern. During operationthe control unit receives the output signals from the microphones and,on the basis of these, adjusts the filter coefficients of the digitalfilters until the predetermined acoustic pattern has been obtained.Loudspeakers in a linear array, in a matrix form and in a honeycombstructure are described in the embodiments.

The directional sensitivity of the known loudspeaker system can becontrolled up to about 1400 Hz for the embodiments with a linear arrayand a matrix arrangement. An upper limit of about 1800 Hz is cited forthe honeycomb structure. This upper limit is inadequate for many audioapplications and it would be desirable to provide a loudspeaker systemwhich can control the directional sensitivity up to frequencies of about10 kHz.

In J. van der Werff, "Design and Implementation of a Sound Column withExceptional Properties", 96th Convention of the AES (Audio EngineeringSociety), Feb. 26-Mar. 1, 1994, Amsterdam, an analogue loudspeakersystem is described in which the individual loudspeakers are arranged atnon-equidistant spacings along a straight line. The gaps between theindividual loudspeakers are calculated on the basis of the criterion ofmaintaining the side lobes of the acoustic pattern transmitted duringoperation so as to be at a suitably low level. The density of the numberof loudspeakers per unit length is greater in the vicinity of theacoustic centre than at a distance away from this.

The primary objective of the present invention is to provide aloudspeaker system which has a controlled directional sensitivity overas wide a frequency range as possible.

A further objective of the invention is to provide a loudspeaker systemwherein the maximum deviation of the directional sensitivity is as faras possible constant over the envisaged frequency range.

To this end, the invention provides a loudspeaker system according tothe type described above, characterised in that the loudspeakers have amutual spacing, which, insofar as physically possible, substantiallycorresponds to a logarithmic distribution, wherein the minimum spacingis determined by the physical dimensions of the loudspeakers used. Bynot making the mutual spacing of the loudspeakers equidistant butadapting it to the frequency requirements, it is possible to control thedirectional sensitivity up to, certainly, 8 kHz. The side lobe level isreduced at the same time. By choosing a logarithmic distribution, themaximum deviation of the directional sensitivity over the envisagedfrequency range is kept as constant as possible and spatial aliasing athigher frequencies is counteracted. Primarily it is not so much the formof the sound pattern as the transmission angle which is controlled.

There are various possibilities for the arrangements. For instance, theloudspeakers can be arranged along a straight line, in which case thesaid distribution extends from a central loudspeaker in one directionalong said line.

As an alternative, the loudspeakers can be arranged along two straightline sections, in which case the said distribution extends from acentral loudspeaker in two directions along the two line sections, whichcentral loudspeaker is located at an intersection of the two linesections.

The two line sections can be on a straight line.

As a further alternative, the loudspeakers can be arranged on two lineswhich cross one another or can be arranged in the form of a matrix.

Preferably, the loudspeakers are identical.

The loudspeakers can be arranged in various rows, each of which isoptimised for a specific, predetermined frequency band. The loudspeakersarranged in said rows can, for example, be of different dimensionsand/or have a different logarithmic distribution.

The filters can be FIR filters or IIR filters.

Preferably, the filters are digital filters which have predeterminedfilter coefficients and are each connected in series with associateddelay units having predetermined delay times, which filter coefficientsand delay times are stored in a memory, for example an EPROM.

The audio signal preferably originates from an analogue/digitalconverter, which also has an input for receiving a background signalcorresponding to the sound in the surroundings. Said analogue/digitalconverter can be provided with an output for connection to at least onedependent ancillary module.

The invention will be explained in more detail below with reference to afew diagrammatic drawings, in which:

FIG. 1a shows an effective, normalised array length as a function of theangular frequency for a distribution of three loudspeakers per octaveband;

FIG. 1b shows the deviation of the opening angle α as a function of theangular frequency for a distribution of three loudspeakers per octaveband;

FIGS. 2a to 2d show various arrangements of loudspeakers in accordancewith the present invention;

FIG. 3 shows a diagrammatic overview of an electronic circuit which canbe used to control the loudspeakers; and

FIG. 4 shows an example of an acoustic pattern.

The present description refers to an array of loudspeakers. Such anarray can be one-dimensional (line array) or two-dimensional (plane).

If the transmitting portion for each frequency component in a soundsignal which is reproduced is proportional to the wavelength of thefrequency component concerned, the array is found to displayfrequency-independent behaviour. Two concepts are important for goodunderstanding of the present invention: the opening angle and thetransmission angle. The opening angle is, by definition, the anglethrough which a sound source can be turned such that the sound pressuredoes not fall by more than 6 dB with respect to the maximum value whichis measured at a fixed point in a plane in which the sound source islocated, and at a distance which is large compared with the physicaldimensions of said sound source. Said angle is indicated by "α" in FIG.4, which figure will be discussed further below. The transmission angleis, by definition, the angle β which the axis of symmetry of thetransmission pattern makes with a plane perpendicular to the axis alongwhich a one-dimensional array is arranged, or with a middle verticalline of the plane in which a two-dimensional array is arranged (FIG. 4).In the case where a two-dimensional array is used, two opening anglesand two transmission angles can be defined for a transmission pattern.

The following relationship applies for the dimensions of the effectiveportion of a linear array having an infinite number of loudspeakers, asa function of the frequency: ##EQU1## where: l(ω)=the effective arraysize,

c₀ =the speed of sound (m/s)

k=a proportionality constant, which is a measure of the opening angle α

ω=angular frequency (rad/s)

The following rule of thumb can be used to calculate the proportionalityconstant k: ##EQU2## where: α is the desired opening angle in degrees.

This relationship for the proportionality constant k has an accuracy ofmore than 90% for k>1.

Because an array in practice does not consist of an infinite number ofloudspeakers but is composed of a limited number of loudspeakers, thearray size l(ω) is quantised. As can be seen from FIGS. 1a and 1b, thisresults in a limited resolution in the opening angle α. FIG. 1a showsthe effective array length (logarithmic) as a function of the angularfrequency (logarithmic 1/3 octave) for a distribution of threeloudspeakers per octave band. FIG. 1b shows the deviation of the openingangle α as a function of the angular frequency for a distribution ofthree loudspeakers per octave band. Of course, this is merely an exampleand the invention is not restricted to three loudspeakers per octaveband.

The criterion taken for calculation of the spacing of loudspeakers isthat the maximum deviation of the directional sensitivity must be keptas constant as possible over the envisaged frequency range. As willbecome apparent below, this can be achieved by providing theloudspeakers used, SP₁, SP₂, . . . , with a logarithmic arrangement withrespect to a central loudspeaker SP₀. This also results inminimalisation of the deviation of the opening angle α andminimalisation of the number of loudspeakers required.

The frequency-dependent variation in a is inversely proportional to thenumber of loudspeakers per octave band and theoretically is 50% for adistribution of one loudspeaker per octave. Preferably, in practice useis made of at least two to three loudspeakers per octave.

If the array size l(ω) in a single dimension is quantised with the aidof n steps per octave band, the following relationship then applies forthe array size: ##EQU3## where: ω_(min) =the lowest reproducible angularfrequency (radians per second) at which the opening angle α is stillcontrolled;

n=number of loudspeakers per octave band;

n_(max) =the total number of discrete steps in a single dimension,depending on the desired frequency range.

For a value of i=0, this gives the maximum physical dimension of thearray, which is dependent on ω_(min) and k(α).

The loudspeaker positions depend on the physical configuration of thearray. Said configuration can be asymmetrical or symmetrical. In thecase of an asymmetrical configuration, the central loudspeaker SP₀ islocated at one side of the array, as is shown in FIG. 2a. The aboveEquation 3 applies for the distance l(i) between the loudspeakerpositions and the central loudspeaker SP₀, which corresponds to alogarithmic distribution. In order to produce such an array, n_(max)loudspeakers are required in one dimension.

FIG. 2b shows a symmetrical arrangement of loudspeakers around a centralloudspeaker SP₀, which is located in the middle. The above Equation 3multiplied by a factor of 1/2 applies for loudspeakers SP₁, SP₂, SP₃, .. . , whilst Equation 3 multiplied by a factor of -1/2 applies forloudspeakers . . . SP₋₃, SP₋₂, SP₋₁. For a symmetrical arrangementaccording to FIG. 2b, 2.n_(max) -1 loudspeakers are needed. It is foundthat the symmetrical arrangement according to FIG. 2b gives a bettersuppression of the side lobe level than does the asymmetricalarrangement according to FIG. 2a.

In fact, FIG. 2b is a combination of 2 array configurations according toFIG. 2a with coincident central loudspeakers. These two separateloudspeaker arrays can also be located on two line sections, which donot lie in the extension of one another.

Instead of the configurations shown in FIGS. 2a and 2b, two-dimensionalconfigurations are also possible. FIG. 2c shows a matrix arrangement ofloudspeakers, in which various loudspeaker arrays according to FIG. 2bare arranged parallel to one another. n_(max) hor.n_(max) vertloudspeakers are present in an arrangement of this type. Here n_(max)hor is the number of loudspeakers in the horizontal direction andn_(max) vert is the number of loudspeakers in the vertical direction.

FIG. 2d shows a two-dimensional configuration with an arrangement in theform of a cross. FIG. 2d shows two loudspeaker arrays according to FIG.2b which are arranged perpendicular to one another with a coincidentcentral loudspeaker SP₀,0.n_(max) hor +n_(max) vert -1 loudspeakers arepresent in the arrangement according to FIG. 2.

Of course, arrangements along other and more lines crossing one anotherare also possible. The only proviso in the context of the presentinvention is that the various loudspeakers SP_(i),j are arranged inaccordance with a logarithmic distribution, for example as defined bythe above Equation 3.

In practice, the loudspeakers have a definitive physical size. Thisphysical size determines the minimal possible spacing between theloudspeakers. Those loudspeakers which, in accordance with the aboveEquation 3, would have to be placed a distance apart which is smallerthan the physical size permits are, in practice, placed in contact withone another. This leads to concessions with regard to the resolution inthe frequency range concerned. Naturally, the concessions with regard tothe resolution are as small as possible if the sizes of the loudspeakersare chosen to be as small as possible. However, smaller loudspeakersusually have poorer characteristics with regard to power and efficiency.Therefore, in practice, a compromise will always have to be made betweenthe quality of the loudspeakers and the concessions in respect of theresolution.

Preferably, all loudspeakers must have the same transfer function.Therefore, all loudspeakers in the one-dimensional or two-dimensionalarray are preferably identical to one another.

It is, however, also possible to use various arrays arranged alongsideone another which are provided with different loudspeakers, in whichcase the dimensions of the loudspeakers and their mutual positions inthe various arrays are optimised for a specific limited frequency band.In that case no concessions have to be made in respect of the resolutionand the power or the efficiency. Of course, this is at the expense ofthe number of loudspeakers required.

FIG. 3 shows a diagrammatic overview of a possible electrical circuitfor controlling the loudspeakers. For ease, only the loudspeakers SP₀,SP₁, . . . , SP_(m) and the associated electronics are indicated in thefigure. Therefore, FIG. 3 corresponds to the loudspeaker array accordingto FIG. 2a. However, similar electronic circuits also apply for otherloudspeaker arrays according to the invention, for example according toFIGS. 2b, 2c and 2d.

Each loudspeaker SP_(i) receives an input signal from a series circuitcomprising a filter F_(i), a delay unit D_(i) and an amplifier A_(i).The filters F_(i) are preferably digital filters of the FIR (FiniteImpulse Response) type or of the IIR (Infinite Impulse Response) type.If IIR filters are used, they preferably have a Bessel characteristic.The coefficients of the filters F_(i) are calculated beforehand andstored in a suitable memory, for example an EPROM. This preferably takesplace during manufacture of the loudspeaker system. The filtercoefficients of the filters F_(i) are then no longer adjusted duringoperation, so that it is then possible to dispense with an electroniccontrol unit which would be connected to the filters F_(i) and the delayunit D_(i) for adjusting the filter coefficients, or the delay times,during operation on the basis of the sound pattern recorded bymicrophones. However, use of such a feedback to a control unit (notshown here) and various microphones, as is disclosed in theabovementioned U.S. Pat. No. 5,233,664, is possible within the scope ofthe present invention.

The delay times for each of the delay units D_(i) are preferably alsocalculated beforehand during manufacture and stored in a suitable chosenmemory, for example in an EPROM. These delay times are then also nolonger changed during operation.

Each of the filters F_(i) receives an audio signal AS via a first outputS_(o1) of an analogue/digital converter ADC. The analogue/digitalconverter ADC receives a first analogue input signal S_(i1), which hasto be converted by the loudspeakers SP₀, SP₁, . . . , into a soundpattern with a predetermined directional sensitivity.

Preferably, the analogue/digital converter ADC is also connected to ameasurement circuit which is not shown, which supplies a second inputsignal S_(i2) which is a measure for the noise in the surroundings.Depending of the level of the noise in the surroundings (that is to saythe amplitude of the input signal S_(i2)), the analogue/digitalconverter ADC automatically adapts its output signal S_(o1) in such away that the sound produced by the loudspeakers SP₀, SP₁, . . . , isautomatically adjusted to the noise in the surroundings.

The analogue/digital converter ADC can also be connected to one or moreancillary modules NM, one of which is shown diagrammatically in FIG. 3.The analogue/digital converter ADC controls said one or more ancillarymodules NM via a second output signal S_(o2).

The number of loudspeakers can be expanded by the use of one or moresuch ancillary modules NM. To this end, the one or more ancillarymodules NM then consist(s) of one or more of the loudspeakerconfigurations according to FIGS. 2a, 2b, 2c and/or 2d or variantsthereof, each of the loudspeakers being provided with a series circuitcomprising a (digital) filter, a delay unit and an amplifier, as isindicated in the upper part of FIG. 3 for the loudspeakers SP_(o), SP₁,. . . .

It is, however, also possible to equip the ancillary module NM only withvarious parallel series circuits comprising a (digital) filter, a delayunit and an amplifier, which series circuits are then connected to theloudspeakers SP₀, SP₁, . . . of the main module according to FIG. 3.With an arrangement of this type, various transmission patterns withdifferent directional sensitivity can be generated with a singleloudspeaker array.

It will be clear to those skilled in the art that the (digital) filtersF₁, the delay units D_(i) and the amplifiers A_(i) do not have to bephysically separate components, but that they can be realised by meansof one or more digital signal processors.

Resolution over a period of about 10 microseconds is found to be asuitable value in order to achieve adequate resolution in respect of thetransmission angle β. Good coherence of the loudspeakers, even at higherfrequencies, is also ensured by this means. This is achieved by using asampling frequency of 48 kHz for the analogue/digital conversion in theanalogue/digital converter ADC and using the same sampling frequency forcalculation of the filter coefficients as well. The delay units D_(i)are fed at a sampling frequency of 96 kHz by doubling thefirst-mentioned sampling frequency. This gives a resolution of 10.4microseconds. Of course, other sampling frequencies are also possiblewithin the scope of the invention.

A loudspeaker array designed in accordance with the guidelines givenabove has a well defined directional sensitivity which is substantiallyfrequency-independent over a wide frequency range, that is to say up toat least a value of 8 kHz. The directional sensitivity is found to bevery good in practice.

It is also possible to design a loudspeaker array in accordance with theguidelines given above with which the transmission pattern is notperpendicular to the axis along which the loudspeaker array is located(or the plane in which said array is located). The opening angle α canbe selected by making a suitable choice for the filter coefficients,whilst any desired transmission angle β can be obtained by adjustment ofthe delay times. In this way, a sound pattern can be directedelectronically. When a one-dimensional loudspeaker array is used, thetransmission pattern is rotationally symmetrical with respect to thearray axis 2. When a two-dimensional loudspeaker array is used, thetransmission pattern is symmetrical according to a mirror image aboutthe array plane. This symmetry can advantageously be used in situationsin which the directional sensitivity of the sound which is generated atthe rear of the loudspeaker array also has to be controlled.

Finally, FIG. 4 shows an example of a (simulated) polar diagram toillustrate a possible result of a loudspeaker array designed accordingto the invention. The opening angle α shown in this figure isapproximately 10°, whilst the transmission angle β is approximately 30°.The arrangement of the loudspeaker array which generates the patternshown is likewise shown diagrammatically. For the sake of convenience,the logarithmic distribution has been dispensed with in this diagram.

What is claimed is:
 1. Loudspeaker system comprising a first set of atleast three loudspeakers (SP₀, SP₁, . . . ), which are arranged along afirst straight line in accordance with a predetermined pattern, eachloudspeaker having an associated filter (F₀, F₁ . . . ), which filtersall receive an audio signal (AS) and are equipped to transmit outputsignals to the respective loudspeakers (SP₀, SP₁ . . . ) such that they,during operation, generate a sound pattern of a predetermined form,characterized in that the at least three loudspeakers (SP₀, SP₁ . . . )of said first set are arranged on locations (l(i)) relative to anorigin, said locations beingdefined by the following equation: ##EQU4##where: l(i)=locations on which a loudspeaker is arranged; the origin isthe location for which i→∞; i=0, 1, . . . , n_(max) -1; c₀ =the speed ofsound (m/s); k=a proportionality constant, which is a measure of openingangle α; n=number of loudspeakers per octave band; n_(max) =the totalnumber of discrete steps in a single dimension, depending on the desiredfrequency range; ω_(min) =the lowest reproducible angular frequency(radians per second) at which the opening angle α is stillcontrolled;and wherein when in accordance with said equationloudspeakers would have to be placed a distance apart which is smallerthan the physical size permits they are placed in contact with oneanother.
 2. Loudspeaker system according to claim 1, characterized by asecond set of at least three loudspeakers (SP₋₁, SP₋₂ . . . ) arrangedalong a second straight line in accordance with an equal equation as thefirst set of at least three loudspeakers, origins of said first andsecond sets being coincident.
 3. Loudspeaker system according to claim2, characterized in that the first and second straight lines coincideand that the first set of loudspeakers (SP₀, SP₁, . . . ) is disposed onone side of said origin and the second set of loudspeakers (SP₋₁, SP₋₂,. . . ) is disposed on the other side of said origin on said straightline.
 4. Loudspeaker system according to claim 1, characterized by aplurality of further sets of at least three loudspeakers, each furtherset arranged along a further straight line in accordance with an equalequation as the first set of at least three loudspeakers, any of saidfurther straight lines being parallel to said first straight line. 5.Loudspeaker system according to claim 1, characterized in that theloudspeakers are identical.
 6. Loudspeaker system according to claim 4,characterized in that the further sets of at least three loudspeakershave been optimized for a specific, predetermined frequency band. 7.Loudspeaker system according to claim 1, characterized in that thefilters (F₀, F₁, . . . ) are either FIR filters or llR filters. 8.Loudspeaker system according to claim 1, characterized in that thefilers are digital filters (F₀, F₁, . . . ) which have predeterminedfilter coefficients and are each connected in series with associateddelay units (D₀, D₁, . . . ) having predetermined delay times, whichfilter coefficients and delay times are stored in a memory, for examplean EPROM.
 9. Loudspeaker system according to claim 1, characterized inthat the audio signal (AS) originates from an analogue/digital converter(ADC), which also has an input for receiving a background signal(S_(i2)) corresponding to the sound in the surroundings.
 10. Loudspeakersystem according to claim 9, characterized in that the analogue/digitalconverter has a further output for connection to at least one dependentancillary module comprising various further loudspeakers which arearranged in accordance with a predetermined further pattern and haveassociated further filters, which filters all receive said audio signaland are equipped to transmit further output signals to the respectivefurther loudspeakers such that they, during operation, generate afurther sound pattern of a further predetermined form, wherein thefurther loudspeakers have a mutual further spacing, which, insofar asphysically possible, substantially corresponds to a logarithmicdistribution, wherein the minimum spacing is determined by the physicaldimensions of the loudspeakers used.
 11. Loudspeaker system according toclaim 9, characterized in that the analogue/digital converter has afurther output for connection to at least one dependent ancillary modulecomprising various parallel series circuits, each series circuitcomprising a filter, a delay unit and an amplifier, and each seriescircuit being connected to a distinct one of said loudspeakers.